1. Work Based Learning Functional Skills Maths
Session 3
Measures, Conversions and Estimations

2. General Advice
Remember: At Level 1 you will only need to work with measures in the metric system. At level 2 you may need to convert between the metric and imperial systems but the numbers to use will be provided for you in the resources. Some slides are titled level 2 only. These indicate extensions that only learners working towards Functional Skills level 2 will need. At both levels you are expected to be able to convert within the metric system without being given any further information, for example change centimetres into metres.

3. Metric Measures
The metric system is the modern system of measurement used Britain.
One obvious way to spot if a measure is metric is if you can add milli- or centi- to the front of it then it fits in the metric system.
Eg, which is metric metre or yard?
You can say millimetre but you cannot have a milliyard so metre is metric but yard id not.
The metric system is in base 10. This means the link between each unit is 10, 100, 1000 and so on. We will apply this to some examples in a minute.

4. Length
The metric unit of length is metre. An example of a metre would be the width of a door.
To describe lengths smaller or larger then this, we still use the word metre, but we put a prefix in front of it to slightly alter its meaning. The same prefixes are used all across the metric system.
Prefix
Meaning
Milli-
1/ a thousandth (1000 times smaller)
Centi-
1/ a hundredth (100 times smaller)
Kilo-
Thousand (1000 times bigger)

5. Metric Prefixes
So if milli- means thousandth. Then a millimetre must mean a thousandth if a metre. That is to say that there are 1000 millimetres in a metre. Remember a millennium is 1000 years.
Centi- means hundredth. So a centimetre must be a hundredth of a metre. That is to say that there are 100 centimetres in a metre. Remember there are 100 years in a century (we looked in session 1 at ‘cent means 100’)
Kilo- means thousand. So a kilometre must be 1000 metres. There are 1000 metres in one kilometre.

6. Millimetre Centimetre Metre Kilometre
Converting within the metric system
Millimetre
Centimetre
Metre
Kilometre
÷10
Here I will use length as the example but the same rules apply for other metric measure we will look at later.
10mm = 1cm
100cm = 1m
1000m = 1km
x10
x100
÷100
÷1000
x1000

7. Converting within the metric system
Convert mm to cm. Remember there are 10mm in 1 cm (you can check this by looking at your ruler) so we must divide by 10.
250mm ÷ 10 = 25cm
790mm ÷ 10 = 79cm
1200mm ÷ 10 = 120cm
2446mm ÷ 10 = 244.6cm

8. Converting within the metric system
Convert cm to m. Remember there are 100cm in 1 m so we must divide by 100. To convert m to cm we must multiply by 100
Centimetre to Metre
480cm ÷ 100 = 4.8m
60cm ÷ 100 = 0.6m
4500cm ÷ 100 = 45m
Metre to Centimetre
3m x 100 = 300cm
7.2m x 100 = 720cm
11m x 100 = 1100cm

9. Links between metric units for length, area and volume
The word metre also appears in area and volume in the form of square metres (m2 ) and metres cubed (m3 ).
Area and volume are calculated using lengths, that is why there is a link between the units used.
We will look at these measure in the next session. For now it is important to learn the summary on the next page, so we can build on it in the next session.

10. Millimetre Centimetre Metre Kilometre Learn this Page!
Copy it out on paper
Summary
Millimetre
Centimetre
Metre
Kilometre
÷10
÷100
÷1000
x10
x100
x1000
10mm = 1cm
100cm = 1m
1000m = 1km
Milli- means thousandth
Centi- means hundredth
Kilo- means thousand

11. Weight
The metric unit of weight is the gram. One gram is about the weight of a paperclip.
Sometimes we need to describe weights that are a lot heavier than a paper clip, so for this we could use kilograms. A kilogram is the weight of a bag of sugar The prefixes used are the same as for length.
We don’t often use centigrams, but we do use milligrams when measuring medicine. Pain-killers usually comes in 500mg (milligram) tablets.

12. Converting within the metric system
Convert grams to kilograms . Remember there are 1000g in 1kg so we must divide by To convert kilograms to grams we must multiply by 1000
Grams to Kilograms
8903g ÷ 1000 = 8.903kg
600g ÷ 1000 = 0.6kg
In weight there is also a metric tonne, which is worth 1000kg
2783kg ÷ 1000 = tonne tonne x 1000 = 67000kg
Kilograms to Grams
3kg x 1000 = 3000g
8.2kg x 1000 = 8200g

13. Milligram Gram Kilogram Tonne Learn this Page! Copy it out on paper
Summary
Milligram
Gram
Kilogram
Tonne
÷1000
x1000
1000mg = 1g
1000g = 1kg
1000kg = 1 tonne
Milli- means thousandth
Kilo- means thousand
A tonne is 1000kg

14. Millilitre Litre Capacity
We can consider capacity to be the amount which an object can hold, or the amount of space the object takes up. It is related to volume.
In the metric system we measure capacity in litres and millilitres. A large fizzy drinks bottle usually contains 2 litres of liquid.
We know from milli- that there are
1000 millilitres in 1 litre
Millilitre
Litre
÷1000
x1000

15. Temperature
In the metric system temperature is measured in degrees centigrade (also called Celsius) (ºc)
0ºc is the temperature that water turns to ice
It is possible to get colder than 0ºc, these colder temperatures are shown with negative numbers eg
-3ºc. Remember -11ºc so colder than -3ºc because it is further below zero.
100 ºc is the temperature water turns to steam
Around 5 ºc is a typical winters day
And about 23ºc is a warm summers day

16. Time We need to use time alongside metric measures.
60 seconds=1 minute hours a day weeks a year
60 minutes = 1 hour days a week months a year
If you are asked to calculate with time, for example finding average journey times, the convert all the timings into the same unit. For example, find the total of:
1hour 43 minutes, 57 minutes, 2hour 8 minutes.
Change them all into minutes first before calculating with them,
1 hour 43min = 60min + 43 min = 103 minutes
2 hours 8 min = = 8 = 128 minutes
You can then add all the minutes together. When we look at average in a few session we will be able to use the total number of minutes to calculate an average time.

17. Learn this Page! Copy it out on paper
Summary
Capacity is the space to fill an object, we often think of it as liquid filling a space. It is measured in litres and millilitres (1 litre = 1000ml)
Temperature is measured in degrees centigrade (also called Celsius) (ºc). You can get minus numbers for temperatures that are colder than freezing
When calculating with time, don’t use minutes and hours and seconds. Convert all the times to the same unit, eg all into minutes

18. Imperial conversions (Level 2 only)
At level 2 you may be expected to convert between metric and imperial measures. But you will always be given the numbers you need for the conversion in the resources or the question itself.
Convert 95cm to inches inch =2.54cm
So you need to use these numbers to make the conversions.
95 ÷ 2.54 = 37.4 inch
An inch must be bigger than a cm because we need 2.54cm to make up 1 inch. So we know that our answer to the conversion must be a smaller number than 95. this is a useful quick check to see if the answer is sensible.

19. Imperial conversions (Level 2 only)
1kg = 2.2 pounds
Convert 40kg to pounds
40 x 2.2 = 88pounds
Convert 45pounds to kg
45 ÷ 2.2 = … rounded to 20kg
When you make a conversion like this, it will involve either dividing, or multiplying by the number in the conversion (in this case 2.2) times if your changing to the unit with that number (eg the 2.2 is pounds, so times by 2.2 to change to pounds) or divide by the number if you want your answer in the other unit.
When you get your answer consider if it is reasonable like we did on the last slide. If 1 kg is 2.2 pounds. Then my answer in pounds should come out larger than the number of kg to equal the same weight. It did so I am happy my answer is reasonable.

20. Estimation
In functional skills, we sometimes have to make assumptions and choices about what is reasonable and sensible.
Consider the example from earlier that a bag of sugar weight 1kg.
How heave do you think a person would be in kg?
How many kg could a person lift easily above their head?
Questions like this have a range of answers that are correct. But you need to make an estimate and write it down on the page in order to answer later questions.

21. Here is an example from a functional skills test paper:
Estimation Example
Here is an example from a functional skills test paper:
You may have an idea the weight of hand baggage airlines allow, or you might think of how many bags of sugar you could carry in a bag.
An answer between 5 and 30kg would be accepted as correct. But select a number for example 15kg. This would be marked correct but it is not the only correct answer.

22. Task
Now you have read through all the examples and written out your revision notes you should complete:
Session 3 Homework – Measures, Conversions and Estimation
Read your revision notes and these slides to help you complete the homework.
Complete the homework task and hand it in to your Functional Skills tutor at your next meeting